---
title: Quantization-Aware Unlearning Methods
url: https://www.emergentmind.com/topics/quantization-aware-unlearning-method
type: topic
---

# Quantization-Aware Unlearning Methods

Quantization-aware unlearning encompasses methodologies designed to robustly remove specific data-derived knowledge from neural networks that employ low-bit quantization for model deployment. As quantization is increasingly used for on-device inference, especially under resource constraints, standard machine unlearning methods tailored for full-precision models are insufficient—quantization can negate unlearning by restoring the “forgotten” knowledge. Two leading quantization-aware unlearning frameworks, QUAIL (“Quantization Aware Unlearning for Mitigating Misinformation in LLMs” [2601.15538]) and Q-MUL (“Robust Machine Unlearning for Quantized Neural Networks via Adaptive Gradient Reweighting with Similar Labels” [2503.13917]), specifically address these challenges through targeted loss design, data preprocessing, and gradient management strategies.

## 1. Challenges of Machine Unlearning Under Model Quantization

Neural network quantization applies a uniform or non-uniform discretization to model weights and activations, typically reducing precision to 2–8 bits. For a given bit-width $N$, the quantization step size is defined as
$$
\Delta = \frac{w_{\max} - w_{\min}}{2^N},
$$
where $w_{\min}$ and $w_{\max}$ specify the range for each quantized tensor. The quantization operator,
$$
Q(w) = \Delta \, \mathrm{Round}\left( \frac{w - w_{\min}}{\Delta} \right) + w_{\min},
$$
induces bucket collapse: weights differing by less than a quantization threshold $\Delta/2$ quantize to the same value.

Standard machine unlearning proceeds by applying small weight updates (e.g., via gradient ascent on the forget set $D_f$). In quantized models, mean absolute updates ($\approx 2.97 \times 10^{-5}$ for GA+GDR on LLaMA-2-7B) are much smaller than $\Delta/2 \approx 0.134$ for 4-bit weights, resulting in $>99.9\%$ bitwise overlap. Consequently, the quantized unlearned model $Q(\Theta')$ is nearly indistinguishable from the quantized original $Q(\Theta)$, restoring the targeted knowledge and undermining privacy and compliance objectives [2601.15538]. This issue is pervasive across quantization schemes (RTN, AWQ, GPTQ, LSQ+) and bit-widths: bucket overlap rises to $100\%$ at 4-bit quantization.

## 2. Frameworks for Quantization-Aware Unlearning

Two principal quantization-aware unlearning approaches have emerged:

- **QUAIL** introduces a logits-space hinge loss to enforce minimum output separation, inducing weight changes large enough to survive quantization.
- **Q-MUL** incorporates “Similar Labels” assignment and “Adaptive Gradient Reweighting” to balance update magnitudes and reduce gradient noise.

### Comparative Table: Key Methods for Quantization-Aware Unlearning

| Framework | Core Technique            | Quantization Addressed   |
|-----------|--------------------------|--------------------------|
| QUAIL     | Logits-space hinge loss  | Output margin $\Delta/2$ |
| Q-MUL     | Similar labels + AGR     | Balanced updates/labels  |

QUAIL is specifically designed for LLMs and language/classification tasks; Q-MUL targets low-bit quantized classifiers and mobile networks.

## 3. QUAIL: Logits-Space Hinge Loss and Algorithmic Structure

QUAIL’s primary innovation is the imposition of a quantization-aware hinge loss:
$$
\mathcal{L}_{\mathrm{hinge}}(z', z) = \frac{1}{K} \sum_{k=1}^K \max\left(0, \frac{\Delta_q}{2} - |z'_k - z_k|\right),
$$
where $z$ and $z'$ are the output logits of the original and unlearned model respectively, for the same input, and $K$ is the number of output classes. Here, $\Delta_q$ is chosen to match the expected quantization logit step, with margin $=\Delta_q/2$ (empirically $=0.5$). This loss penalizes insufficient logit separation, promoting weight updates exceeding the quantization bucket threshold.

The overall QUAIL objective is
$$
\mathcal{L}_{\mathrm{QUAIL}} = \alpha \mathcal{L}_{\mathrm{forget}} + (1-\alpha) \mathcal{L}_{\mathrm{retain}} + \gamma \mathcal{L}_{\mathrm{hinge}},
$$
where $\alpha$ and $\gamma$ adjust the tradeoff between forgetting, retention, and quantization robustness.

**Algorithmic workflow** entails:
- Caching target logits for all forget examples to avoid redundant computation.
- Applying the hinge loss selectively, with gradient sparsity where logit separation is insufficient.
- Updating parameters via:
  ```
  θ_un ← θ_un - η·∇[α·L_forget + γ·L_hinge]
  θ_un ← θ_un - η·∇[(1-α)·L_retain]
  ```
This mechanism ensures weight updates consistently cross quantization bucket thresholds.

## 4. Q-MUL: Similar Labels and Adaptive Gradient Reweighting

Q-MUL addresses two distinct limitations in quantized MU:

- **Noise amplification from random labels:** Assigning random labels to $D_f$ (the “random label” baseline) injects orthogonal gradients with near-zero model probability, often flipping weights by entire quantization steps and resulting in high error and instability. Q-MUL computes a “semantically closest” incorrect label $k_{sl}$ for each forget example by minimizing the absolute difference in softmax outputs:
  $$
  k_{sl} = \arg\min_{k \neq y_i} |p_Q(k|x_i;\theta_q) - p_Q(y_i|x_i;\theta_q)|.
  $$
  The cross-entropy loss is then applied to $(x_i, k_{sl})$ rather than $(x_i, y_i)$.

- **Gradient imbalance in discrete training:** The quantization process and straight-through estimator (STE) zero many parameter gradients, creating significant gradients magnitude imbalance between forget and retain sets. Adaptive Gradient Reweighting leverages the $\ell_2$ norms of the two sets’ gradients
  $$
  G_f = \mathbb{E}[\|\nabla L_{\mathrm{forget}}\|_2], \quad G_r = \mathbb{E}[\|\nabla L_{\mathrm{retain}}\|_2],
  $$
  to define weighting factors $\alpha_f=G_r/(G_f+G_r), \alpha_r=G_f/(G_f+G_r)$ in the objective. Updates are performed within a quantization-aware training (QAT) loop:
  $$
  \theta_q^{t+1} = \text{Quant}\Big(\theta_q^t - \eta_t \nabla_\theta L_{\mathrm{weighted}}(\theta_q^t)\Big),
  $$
  mitigating the imbalance and maintaining stability across discrete parameter changes.

## 5. Empirical Evaluation and Metrics

QUAIL and Q-MUL are empirically assessed across challenging benchmarks and quantization settings.

**QUAIL:** Evaluated primarily on language (MUSE NEWS) and Twitter Misinformation datasets using LLaMA-2-7B as base architecture (4-bit and 8-bit post-training quantization). Key metrics:

- **VerMem (M1):** average ROUGE-L F1 (lower is better)
- **KnowMem$_f$ (M2):** ROUGE on QA pairs from forget set (lower is better)
- **PrivLeak (M3):** AUC gap vs retrain (closer to 0 is better)
- **KnowMem$_r$ (M4):** QA accuracy on retain set (higher is better)

GA+GDR attains near-perfect forgetting in FP16 but exhibits $24.36$ VerMem degradation at 4-bit; QUAIL limits this degradation to $\sim9$ points and restores privacy metric M3 $\approx 0$, with high retention (M4 $\approx 50$) under 4-bit quantization [2601.15538].

**Q-MUL:** Assessed on image classification datasets (CIFAR-10/100, SVHN, Tiny-ImageNet) using ResNet-18 and MobileNetV2 under LSQ+ QAT, and compared to gold-standard retraining and prior MU baselines. Performance is measured using Forget Accuracy (FA), Retain Accuracy (RA), Test Accuracy (TA), Membership Inference Attack accuracy (MIA), and Average Gap (AG). Q-MUL achieves the lowest AG ($3.11$ compared to RL $9.89$, SalUn $6.05$) and maintains balanced FA/RA/TA versus retraining [2503.13917]. Similar label assignment and AGR step contribute critically to these improvements.

| Method   | FA    | RA    | TA    | MIA    | AG   |
|----------|-------|-------|-------|--------|------|
| Retrain  | 74.76 | 99.98 | 72.43 | 13.36  | 0.00 |
| RL       | 68.51 | 98.91 | 69.47 | 85.62  | 9.89 |
| SalUn    | 82.22 | 98.71 | 67.38 | 66.78  | 6.05 |
| Q-MUL    | 75.71 | 97.89 | 67.27 | 52.11  | 3.11 |

## 6. Limitations and Open Problems

Both frameworks display sensitivity to hyperparameters governing loss tradeoff ($\alpha$, $\gamma$ in QUAIL; learning rate and batch schedules in Q-MUL). For QUAIL, too low a $\gamma$ fails to cross quantization thresholds, while excessive $\gamma$ impairs utility retention. Q-MUL exhibits modest compute overhead ($\approx 1.1\times$ RL) due to gradient norm statistics calculation.

Deployment constraints include focus on uniform post-training quantization (QUAIL) and layering limitations (embeddings and layer-norm not quantized), while Q-MUL has been mainly explored in classification networks. Neither approach currently provides worst-case or certified bounds on adversarial knowledge recovery post-quantization; future work may address theoretical guarantees and broader domain adaptation.

A plausible implication is that direct extension to detection, generative, and language modeling tasks (not yet covered by Q-MUL) could further broaden quantization-aware unlearning applicability, but may require new objective designs sensitive to task structure.

## 7. Significance and Future Directions

Quantization-aware unlearning establishes a necessary paradigm for enforcing data privacy and compliance (e.g., “right to be forgotten”) in on-device inference regimes. By explicitly characterizing quantization-induced failures of standard unlearning, and introducing loss, label, and gradient management tailored to discrete parameter spaces, frameworks like QUAIL and Q-MUL set state-of-the-art benchmarks for forgetting efficacy and utility retention in quantized networks.

Future directions include extension of quantization-aware methods to mixed-precision settings, systematic study under quantization-aware training (QAT), and development of theoretical security/robustness guarantees for persistent unlearning in quantized models.

Source: https://www.emergentmind.com/topics/quantization-aware-unlearning-method